Boatcarpenter
I uploaded TM's for two versions:
TM 11-5915-223-12, for the MX-7777A/GRC (which is called the MX-7778/GRC when installed with the mount, cables, etc.). It does not have a battle override switch, and the two output connections are on the same side.
TM 11-5915-224-14, for the MX-7778A/GRC (which is called the MX-7777B/GRC when installed wtih the cables, etc.). It has the battle override switch and there is one output connection on each side.
I also uploaded TM for installing the VRC-12 series in all vehicles (specifics of various installation kits are included in the kits)
TM 11-5820-401-20-1, org. manintenance (and installation)
for additional ideas:
TB 11-52820-890-20-8 covers installation of SINCGARS radios in M35, etc. some of the cable techniques should be similar.
Hope this helps.l
The TM's should answer most of your questions.